Canals are used throughout the world to deliver water from where it is available to where it is needed. Because the costs of building a high-capacity canal are significantly lower than the costs of building a pipeline of equal capacity, canals and open channels are the primary conveyance device for water for agricultural production.
Water delivery canals are generally considered to be a series of sloping pools. Of the several pools which make up most canals, a delivery pool is said to be the pool from which a given demand is initiated. Conveyance pools are all the pools upstream from the delivery pool, which pools transfer the change in flow required by the change in demand. A pool can be either or both a conveyance pool and a delivery pool. Further a sloping pool may be formed with either a level or sloping top.
A major concern facing operators and users of these canals is the scheduling and delivery of water according to the user's needs. This is the problem of canal control.
The earliest canal control systems were based on the theory of upstream control of the canal. A major problem with upstream canal control is that the user (e.g., a farmer) cannot initiate, terminate or modify the flow rate of water at the point of delivery. Instead, the flow rate in the canal is controlled from the headworks, and deliveries to users are scheduled. Since it is often the case that delivery needs and scheduled deliveries do not coincide, a canal operated by schedule under upstream control not only wastes water, but is inaccurate and nonresponsive to changes in user needs. To overcome these problems, workers in the art have been trying for many years to make downstream control a practical reality. Downstream control, as used herein, refers to a canal control methodology which is literally operated or controlled by the user from the downstream part of the canal where the user's turnout is located. To date none of the downstream control methodologies have proven both practical and reliable on a wide variety of existing canals.
By way of further defining the prior art, upstream control generally works in the following manner: To fill the user's water order, the canal operator controls the canal flow starting at the headworks. This control then works in the downstream direction. Each user is required to give some advance notice of desired deliveries so that the canal's schedule can be assembled from all of the users' demands. The canal schedule must accommodate travel times of several hours to several days from the headworks to the user's point of delivery, or turnout. The water provided according to the user's request is hence not available to that user until the travel time from the headworks has elapsed. A major problem with upstream control methods is the fact that they rarely deliver accurate amounts of water to the user. A second major problem is that changes in user needs cannot be timely accommodated. Finally, upstream control wastes water, creating both water shortfalls and surpluses.
In contrast to upstream control, according to the tenets of downstream control, the canal operator would not necessarily be notified in advance of user demands or rejections. Indeed, in the best implementation of this methodology, changes in user demands at any point in the canal would have no impact on deliverability of water to any other user. Instead, an ideal downstream control method would ensure that sufficient water was available for all users at all times with neither water surpluses nor shortfalls to contend with. To date, efforts to implement this ideal downstream controller have not met with success for several reasons enumerated below.
Where price is no object, particularly for very large water distribution systems it has been possible, at significant expense, to derive suitable customized control systems. However, for more modest distribution systems, where price versus functionality is a consideration, methodologies for canal control have not been sufficiently effective.
Efforts by others to implement downstream control of such canals have generally utilized two broad strategies: role-based controllers and control theory-based controllers. Rule-based controllers use a pre-defined set of control actions which are implemented responsive to some sensor input from the canal. Control theory-based controllers use control theory to generate control actions based on canal sensor inputs. Prior to discussing the shortcoming of these prior art methodologies, it is instructive to examine how canals respond to changes in demand and to compensating flows.
If more water is drawn from a pool than flows into it, the pool eventually runs dry. A pool surface level at the pool's downstream end, and showing such an uncompensated demand over time is shown at FIG. 1. Conversely, if less water is drawn from a pool than flows into it, the pool eventually overflows. A second pool surface level showing an uncompensated rejection is shown at FIG. 2. If however, the increased demand is met with an instantaneous and equal increase in inflow, as shown in the hydrograph shown in FIG. 3, a pool surface level such as depicted at FIG. 4 results. This increased inflow is termed a "flow-compensating in-flow".
Most prior art canal control methodologies rely on the use of a setpoint to provide a data point for canal control. In the simplest example, a level setpoint implemented at some point in the canal tells the canal controller if the water is either too high or too low in the pool. The controller then takes the appropriate control action to restore the water level at the setpoint to the desired level. Setpoints may be established at any point in a pool, and each of such locations has its advantages and disadvantages.
Study of FIGS. 3 and 4 makes it apparent that while the flow-compensated inflow prevents the pool from running dry (at least in this pool), the level of the pool at the setpoint location is decreased (in this case, the setpoint is positioned at the downstream end of the pool). This is due to the phenomenon illustrated in FIG. 5. As shown in that figure, as additional inflow is input to overcome the increased demand, the pool surface profile pivots with the additional inflow. This is due to the additional energy, and hence the steeper surface slope, which is necessary to sustain the larger flow. In order to both sustain the increased flow and to maintain the original level of the canal at the downstream end of each pool (hereafter referred to as the setpoint target depth), it is necessary to increase the volume of the pool in addition to increasing the inflow. Maintaining control of a canal, or the pool of a canal, is therefore seen to be a problem having two components. First, inflow must be changed to reflect changes in outflow, i.e. there must be a flow-compensating inflow. Indeed, inflow must equal outflow or the pool either runs dry or overflows; i.e., there must also be a volume-compensating inflow. Secondly, pool volumes must be adjusted to maintain the setpoint of the canal.
Referring now to FIG. 6, the surface profile of a pool having an upstream setpoint pivots about that setpoint, and the surface level at the downstream end of the pool drops with an increase in throughflow. FIG. 7 shows a pool with a midpool setpoint. Here, the surface profile also pivots about the setpoint, and with an increase in throughflow the surface level at the downstream end of the pool also drops, but the surface level upstream of the pivot point rises. Finally, FIG. 8 shows a pool with a downstream setpoint, the situation previously illustrated in FIGS. 1 through 5; once again, changes in throughflow cause the surface profile to pivot about the setpoint, and changes in throughflow result in changes in pool surface level at the upstream end of the pool.
Some of the earliest prior art efforts at downstream control utilized setpoint locations at the upstream end or middle of the pools. This is not possible however with pools which have sloping tops. With sloping top canals the setpoint location must be at the downstream end of the pool or the water will overflow the canal banks when the surface profile pivots counter-clockwise in response to a decrease in throughflow.
As shown in FIG. 4, if only the increased inflow is compensated, the pool volume remains constant, the pool surface pivots, and the setpoint target depth (i.e., at the downstream end of the pool) is abandoned. Abandoning the setpoint target depth means that control of the pool is abandoned.
The hydrograph of a pool which is compensated both for flow and volume following an increase in demand is shown at FIG. 9, and pool depth at the setpoint location and the volume of that pool is shown at FIG. 10. In contrast, FIG. 11 depicts an example of a rejection which is compensated both for volume and flow.
To establish and maintain control of canals, some prior art control methodologies utilized relatively few inputs, but made use of vastly more complex mathematical descriptions of the dynamics of pool flows. Among the best mathematical models of pool flow dynamics are the "de St. Venant" equations, which relate time, flow and depth at any point in the pool or the canal. While they are correct, they are very complex and difficult to simplify. They are particularly difficult to linearize in any effective manner to provide applications using control rules.
Once the depth at the setpoint location changes, the control action required of a pool controller is to change the pool's inflow (at the upstream end). This control action (the change in inflow) sends a wave down the pool. The effect of the control action on the pool depth at the setpoint location (the downstream end) is delayed by the wave's travel time down the pool. This effect is further complicated by the fact that the wave is attenuated as it travels down the pool. Since prior art controllers utilize the depth at the setpoint location as the sole or primary input for control, they must contend with this lag time and attenuation and are therefore less effective. These prior art controllers must "wait" to determine if a given control action was sufficient, insufficient or excessive.
FIG. 10 depicts an example of this problem. As shown in that figure, volume compensation is completed in this exemplar pool at approximately t+40 minutes, or 30 minutes after the increase in demand is initiated at t+10 minutes. Recovery of depth at the setpoint location is however not completely effected until t+52 minutes, or 12 minutes after volume compensation is complete.
In attempting to manage the compensating inflow as a monolithic entity in the face of significant lag time and wave attenuation between control action and ultimate effect, the prior art must provide significant ongoing control action. It will be immediately appreciated then that the prior art attempts to manage a very complex problem, in that prior art controllers must allow for delay and attenuation, thereby further complicating the controller's rule or instruction set.
Pool controllers according to the prior art must either control the canal as a whole, or control only a portion of the canal. The former case is a complex and computationally huge problem. The latter case leaves the uncontrolled balance of the canal at the mercy of seemingly random, but significant, hydraulic influences which come from outside the controller's domain. This means that every event in any pool effects the pools adjacent thereto. Thus, every event in every pool has some effect on the entire canal. These external influences are difficult to manage, especially in canals with poor controllability. Furthermore, the prior art has failed to adequately quantify these influences, precluding the ability to transmit them to adjacent pool controllers electronically.
Unless a means is found to hydraulically de-couple the several pools of a canal, a canal controller must either control all the influences in the entire canal with a monolithic set of rules or equations. Alternatively, a controller must control portions of the canal without regard to conditions in other pools. The former case is a formidable computational effort. The latter case means of course that the canal operator and users must suffer the consequences of significant exogenous influences coming from adjacent and independently controlled parts of the canal. It is well documented that the latter option tends to magnify control problems in the upstream direction.
Taken in sum, the above difficulties have generally precluded the economical fielding of a downstream canal methodology useful over a variety of canals. This is especially true of "difficult" canals. Indeed the prior art does not define those factors which make a canal system controllable, and to allow for them. In general, efforts by other workers in the art have targeted the control problems which pertain to an existing pool, or a hypothetical pool created by averaging several of the characteristics of many existing pools. One example of this "average" pool consisted of combining the geometries of some one hundred pools and finding their arithmetic mean. The resultant "average pool" provided by happenstance a very benign control environment for the controller created in that study to control. This effort then completely disregarded the real-world case where one or more pools in a canal may well be especially challenging from the control perspective. This means that there is little prior art methodology for determining to what extent a given canal is even susceptible to control.
Another problem faced by many prior art downstream control methodologies is that they apply only to canals having level tops, but may not be implemented on sloping top canals. Worldwide, the majority of irrigation canals are built with a sloping profile. Most of these canals have tops which are approximately parallel with the floor, or invert, profile. Hence the tops of most water delivery canals are sloping in profile, and furthermore, most utilize downstream setpoints, where at near-zero flows the canal will not overflow its banks. In order to be an economically feasible alternative to current upstream control methodologies, a downstream control method must be implementable as a retrofit on existing sloping top canals at minimal cost: i.e., without requiring the rebuilding of the canal.
As a final problem exacerbating the computational effort required by most prior art downstream controllers, the methodology whereby the desired inflow is implemented at the upstream gate is seldom idealized. Because the direct measurement of flow in a canal is both problematic and expensive, it is common practice in the prior art to attempt to control inflows by simple position of the inflow gate leaf itself. This methodology fails to account for the fact that a variety of conditions exist which determine the flow through an inflow gate, and gate position, or orifice size, is only one of them.
There are other generalized problems encountered by prior art downstream control theory or rule-based controllers. Controlling the canal as a whole, using numerous inputs from the throughout the canal system is problematic and expensive. It is outside the capability of rule-based controllers due to the sheer complexity of the problem unless control dynamics are limited or expensive in-line reservoirs are utilized. This problem is also difficult to solve using control theory-based controllers both because of problem complexity and because the required rule matrices become very large and are hence difficult to timely solve with modest computer hardware. When some form of local control is implemented, then both rule-based and control theory-based controllers must contend with the interactions between the independently controlled canal sections. The prior art has failed to adequately manage these problems. Furthermore, the prior art has failed to appreciate those factors which affect the controllability of a canal. It therefore follows that the prior art cannot judge how effective the control methods taught thereby operate in the face of those factors. Prior art control systems further utilize dynamic control constants which are difficult both to derive and to tune after controller deployment.
In addition to shortcomings common to both rule-based and control theory-based controllers, there are problems which are unique to the former. Some prior art rule-based downstream controllers utilize an ambiguous rule set. These rule set ambiguities tend to evince themselves at interfaces between cases, i.e., where slight variations in sensor input cause the selection of one case over another. If the two cases possible for selection produce significantly different responses, the system is often led to dithering and possible loss of control.
Prior art control theory-based controllers also have some problems unique thereto. First, modern control theory has little or no inherent ability to properly manage the spatial attributes of the controlled system. Control theory is focused on time-based system dynamics. The previously discussed problems of lag time and wave attenuation which separate control action from the controlled element are very difficult to manage. Second, the mathematics that properly describe the flow dynamics are complex and difficult to simplify in an effective manner. This is especially so since pool flow rates are not practically available as inputs to the control system.
Finally, it will be appreciated that gaining and maintaining effective control of the entire canal is significantly more difficult than controlling each pool of the canal. If each pool in the canal were accurately controlled, it follows that the canal as a whole must be accurately controlled.
The preceding discussion reveals several weaknesses in prior art downstream control methodologies. A canal controller which provided downstream control for canals and was easily and economically implementable on a wide variety of existing canal systems, including canals with sloping tops, would present significant advantages in water economy and management over prior art methodologies. In order to be fully implementable, such a controller must simplify the computational effort required of prior art controllers. This simplification could come from several sources. A first area for improvement over the prior art is that the desired controller should use rule-based control in order to minimize computational requirements. Next, recognizing that compensating inflows may be segregated as flow-compensating and volume-compensating, substantial simplification could be realized if the inflow were treated by the controller as two separate actions.
If pool inflows could be determined by their flow rate as opposed to a change in inflow based on inflow gate leaf position, further accuracies, and economy of computational effort, would accrue to a controller which utilized such a methodology. More significantly, if pool inflows are controlled, then the pools of the canal are in effect hydraulically de-coupled, so that each pool behaves independently.
If demand changes were transmitted electronically, several additional benefits would accrue. First the delay time inherent in wave travel time would be obviated. From this it follows that the controller computational effort could be greatly simplified. By electronically transmitting demand changes, the several pools of the canal can be controlled separately. Because the controller could then concentrate on attaining and maintaining control of one pool in the canal at a time, such control becomes a real feasibility. It follows then that if control of each pool of the canal is realized, control of the canal as a whole must ensue: i.e., each pool is de-coupled hydraulically, independently controlled, and in essence re-coupled electronically.
The ideal canal controller should include a methodology whereby the difficulty of controlling any given pool is determinable. Finally, an ideal pool controller should be implementable on existing sloping top canals without expensive rebuilding of those canals.